Importance of modelling hERG binding in predicting drug-induced action potential prolongations for drug safety assessment

Reduction of the rapid delayed rectifier potassium current (I Kr) via drug binding to the human Ether-à-go-go-Related Gene (hERG) channel is a well recognised mechanism that can contribute to an increased risk of Torsades de Pointes. Mathematical models have been created to replicate the effects of channel blockers, such as reducing the ionic conductance of the channel. Here, we study the impact of including state-dependent drug binding in a mathematical model of hERG when translating hERG inhibition to action potential changes. We show that the difference in action potential predictions when modelling drug binding of hERG using a state-dependent model versus a conductance scaling model depends not only on the properties of the drug and whether the experiment achieves steady state, but also on the experimental protocols. Furthermore, through exploring the model parameter space, we demonstrate that the state-dependent model and the conductance scaling model generally predict different action potential prolongations and are not interchangeable, while at high binding and unbinding rates, the conductance scaling model tends to predict shorter action potential prolongations. Finally, we observe that the difference in simulated action potentials between the models is determined by the binding and unbinding rate, rather than the trapping mechanism. This study demonstrates the importance of modelling drug binding and highlights the need for improved understanding of drug trapping which can have implications for the uses in drug safety assessment.


SYNTHETIC DRUGS
The parameter values of the synthetic drugs are taken from Li et al. (2017). The parameter values for each synthetic drug are given in Table S1. Table S1. Parameter values of the SD model for all synthetic drugs, taken from Li et al. (2017).

PROTOCOLS
The Milnes protocol used in this study is modified from Milnes et al. (2010) by Li et al. (2017). The modified Milnes protocol was repeated with a depolarisation step to 0 mV from the holding potential of −80 mV. The 0 mV step was held for 10 s before repolarising back to −80 mV for 15 s in between pulses. While the depolarisation step allows the binding of drug compounds to the channel, the 15 s holding potential in between pulses allows nontrapped drugs to unbind from the channel, thus reducing the inhibition effect on the current.
The Pneg80, P0, and P40 protocols from Gomis-Tena et al. (2020) are used to assess the dependency of the SD model and the CS model comparison on the calibration protocol. The Pneg80 protocol was held at a holding potential of −80 mV, then depolarised to 20 mV for 0.5 s before a short pulse of −50 mV for 0.2 s. The time period of the protocol was 5.4 s. The P0 and P40 protocols were both held at −80 mV holding potential before depolarising to 0 mV and 40 mV respectively for 5 s. After that, a short pulse of −60 mV was applied for 0.2 s. Both these protocols had pulse length of 5.2 s.

APD 90 VALUES COMPARISON BETWEEN THE AP-SD MODEL AND THE AP-CS MODEL FOR ALL SYNTHETIC DRUGS
The model comparison is repeated for all 12 CiPA training drugs, as listed in Table S1.   The sensitivity analysis was performed on the Hill coefficient n for all synthetic drugs. The Hill coefficient was sampled from a range of the minimum and maximum of n of all synthetic drugs. The distribution of the RMSD for each drug is shown Figure S11A. Figure S11B shows the difference in RMSD between the RMSD of the synthetic drug and the RMSD of the synthetic drug with the Hill coefficient changed for all simulations performed. The RMSD differences had a mean of 4.313± 4.832 ms. Figure S12. A different viewing angle of Figure 7B. (A) The APD 90 differences for combinations of V half−trap , K max and K u parameters. The color of the markers indicate the signed RMSD of each virtual drug in the parameter space. (B) The grey circles are parameter value combination where the signed RMSD is between −30 ms and 30 ms. The triangles are the synthetic drugs taken from Li et al. (2017), color coded with their signed RMSD value. These triangles are projected to the K max -K u plane as red circles for better visualisation.

SENSITIVITY ANALYSIS: DIFFERENT VIEWING ANGLES
The parameter values for all 12 synthetic drugs are taken from Li et al. (2017). Of all synthetic drugs, dofetilide, ranolazine, sotalol, and mexiletine showed small APD 90 differences between the AP-SD model and the AP-CS model. Cisapride showed higher APD 90 values when it is added to the AP-CS model. The remaining synthetic drugs all caused higher APD 90 values with the AP-SD model: bepridil, terfenadine, verapamil, quinidine, chlorpromazine, ondansetron, and diltiazem. Figure S13. The APD 90 differences for combinations of K max and K u at three V half−trap values. The colour of the markers indicate the signed RMSD of each virtual drug in the parameter space. Figure S14. The APD 90 values for randomly chosen K max and K u for three V half−trap values. The grey markers are repeats of the other panels for a better comparison.

APD 90 AT DIFFERENT V half-trap
In Figure 7, changing V half−trap does not change the behaviour of the APD 90 differences. Indeed, the APD 90 differences for three different V half−trap with the full range of the K max and K u axes are similar ( Figure S13). However, it does not imply that V half−trap has no effect on the action potentials. Figure S14 shows the APD 90 values for the same set of V half−trap values as in Figure S13, with the same K max and K u across all panels. The RMSD calculated for the three virtual drugs in Figure S14 are 57.15 ms, 58.88 ms, and 30.29 ms, indicating that the RMSDs are similar (difference between the RMSDs are < 30 ms) but the APD 90 s are different.